The Design Of Generating Function Algorithm And Application In Formation Reconfiguration Of Spacecraft

With the rapid development of science and technology and human exploration of space resources,technical level of single spacecraft has reached an unprecedented height.Space applications of spacecraft also move from single spacecraft to multi-spacecraft.Spacecraft formation flying is one of the important research directions.Although the research in this field is very rich,there are still many problems to be solved urgently,such as the configuration design of formation flying spacecraft and the optimal control of formation reconfiguration,etc.This paper studied the two-point boundary value problem for relative motion of spacecraft basing on the dynamic model of the spacecraft formation flying relative motion and spacecraft relative motion Hamilton model with analytical dynamics.And the optimal control problem in formation reconfiguration of formation flight spacecraft was studied by the method of generating function solution.According to the Hamiltonian theory of analytical mechanics,this paper derived the Hamilton-Jacobi equation and the generating function and canonical transformation.On this basis,the method of solving the numerical solution of the coefficient of the generation function was deduced by Taylor series approximation,and the numerical solution of the generation function was applied to the solution of the relative two-point boundary value problem.Based on the Hamiltonian theory of dynamic equations and analytical mechanics,the Hamilton system model of relative motion of formation flight was established.Then,using the method of generating function,the formation reconfiguration problem of formation flying spacecraft based on these two models is solved and simulated.Based on the Hamilton model established on the basis of the dynamic model,the formation of flight formation is studied.The optimal control law in the process of formation flight formation and the change of the motion state and the optimal motion trajectory of the spacecraft relative to the main spacecraft under the optimal control law were obtained by using the method of generation function and simulation analysis combined with examples.Based on the Hamiltonian system model established directly by analytical mechanics,the problem of formation reconfiguration of formation flight spacecraft was studied.Combining with the example and the simulation analysis,the effects of formation adjustment time and different end position on the energy increment in the initial position and the energy consumed in the process of formation reconfiguration were analyzed.